Definition talk:Absolutely Convergent Series

Definition makes sense in the more general case of a normed vector space. --Lord_Farin 10:31, 6 January 2012 (EST)

Sounds good. As long as we keep the reference to number sets (so that real analysis etc. can be followed through without recourse to heavier equipment than necessary) then no worries. --prime mover 13:27, 6 January 2012 (EST)

This definition makes sense in the most general case of a normed semigroup. The proof that an absolutely convergent series is convergent goes through for a complete normed abelian group (nothing whatsoever about vector spaces appears in it). I'm not sure yet what properties are required for absolute convergence to imply that every rearrangement of a series converges to the same value. --Dfeuer (talk) 17:36, 1 August 2013 (UTC)